This project investigates six fundamental problems in biology: (1) the role of dynamic patterns in embryology and evolution, (2) the kinetics of enzymes located in cell membranes, (3) the kinetics of enzymes derived from malignant and normal cells in culture, (4) mathematical modeling of isoelectric focusing studies, (5) thermodynamics of bioenergetic mechanisms in mitochondria, and (6) development of a new paradigm for biological modeling based upon topological representation and use of network modeling languages. Simulation on digital computers, particularly with network modeling languages, numerical solution of differential equations, and nonlinear regression analysis are the main tools in these investigations. While these problems are diverse in their biological background, they all share in a common basis of mathematical and physical content through the role played by conservation laws and the mathematical methods involved in their resolution.